An h-principle for algebraic bundles and applications

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• Alexis Aumonier (Cambridge)
• Wednesday 18 October 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

A homotopy principle (h-principle for short) often takes the form of a theorem approximating the topology of a space of solutions of a differential equation via homotopical methods. In this talk, I will describe an h-principle for sections of algebraic vector bundles on projective complex varieties subject to differential relations. Combined with some algebraic topology, I will show how it can be used to compute parts of the cohomology of various spaces from classical algebraic geometry. Examples include: the locus of smooth hypersurfaces in a very ample linear system, spaces of smooth complete intersections, and spaces of holomorphic maps to projective spaces.

This talk is part of the Differential Geometry and Topology Seminar series.

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